论文标题
多种学习的数学基础
The Mathematical Foundations of Manifold Learning
论文作者
论文摘要
基于以下假设，即人们观察到的数据位于嵌入在较高维度的空间中的低维歧管上的假设。本文提出了关于流形学习的数学观点，深入研究了内核学习，光谱图理论和差异几何形状的交集。重点放在图形和歧管之间的显着相互作用上，这构成了广泛使用的歧管正则化技术的基础。这项工作是为广泛的数学受众而言可以访问的，包括有兴趣理解流行流行的流形学习算法和降低维度降低技术的定理的机器学习研究人员和从业人员。
Manifold learning is a popular and quickly-growing subfield of machine learning based on the assumption that one's observed data lie on a low-dimensional manifold embedded in a higher-dimensional space. This thesis presents a mathematical perspective on manifold learning, delving into the intersection of kernel learning, spectral graph theory, and differential geometry. Emphasis is placed on the remarkable interplay between graphs and manifolds, which forms the foundation for the widely-used technique of manifold regularization. This work is written to be accessible to a broad mathematical audience, including machine learning researchers and practitioners interested in understanding the theorems underlying popular manifold learning algorithms and dimensionality reduction techniques.
